I am not familiar with nanoparticle science by any means, but I did read through the paper and give an attempt at an answer.
To explain the spatial mismatch between optical hot-spot and heat source hot-spot, they present Figure 3 (comparison between experiment and simulation) and make this comment:
Optical hot spots usually come from tip effect and charge accumulation at the metal interface [Figs. 3(k) and 3(l)], whereas heat arises on the contrary from areas where charges can freely ﬂow [Figs. 3(m) and 3(n)].
In metals, electrons make the dominant contribution to thermal conductivity (phonon contribution becomes more significant for impurity samples or insulators) [Kittel, Introduction to Solid State Physics]. And Equation (2) makes it clear that heat source density is related to electric current density.
Now if you compare Fig 3(k) and 3(m) for longitudinal polarization, you see that current density is focused in the middle, because the strong surface charges at the middle gap, and the left and right extremities inhibit free current. On the other hand, electric field is very strong at the "gap" region due to the (+) and (-) surface charges, so optical hot-spot appears in this "gap" region. They use a two-photon process which is nonlinear, so the signal will be very sensitive to the strength of the electric field.
In summary, I think it all has to do with the accumulation of surface charges, which can give rise to strong local electric field (good nonlinear optical signal), but which inhibits free flow of electrons, the dominant heat carrier.